Home
Class 12
MATHS
Let g(x)=2f(x/2)+f(1-x) and f^(primeprim...

Let `g(x)=2f(x/2)+f(1-x)` and `f^(primeprime)(x)<0` in `0<=x<=1` then g(x)

A

(1/2, 2)

B

(4/3, 2)

C

(0, 2)

D

(0, 4/3)

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    DISHA PUBLICATION|Exercise EXERCISE - 1|65 Videos

  • APPLICATION OF INTEGRALS

    DISHA PUBLICATION|Exercise EXERCISE-2: CONCEPT BUILDER|30 Videos

Similar Questions

Explore conceptually related problems

Let g(x)=2f((x)/(2))+f(1-x) and f'(x)<0 in 0<=x<=1 then g(x)

Let g(x)=2f(x/2)+f(2-x) and f''(x)<0 , AA x in (0,2) .Then g(x) increasing in

Let g(x)=f(x)+f(1-x) and f'(x)<00<=x<=1. Then

Let f(x+y)=f(x) f(y) and f(x)=1+(sin 2x)g(x) where g(x) is continuous. Then, f'(x) equals

If F(x)=f(x)dotg(x) and f^(prime)(x)dotg^(prime)(x)=c , prove that (F")/F=f^(primeprime)/f+g^(primeprime)/g+(2c)/(fg)&F^(primeprimeprime)/F=f^(primeprimeprime)/f+g^(primeprimeprime)/g

Let g (x )=f ( x- sqrt( 1-x ^(2))) and f ' (x) =1-x ^(2) then g'(x) equal to:

Let f(x) = (e^(x) - e^(-x))/(2) and if g(f(x)) = x , then g((e^(1002) -1)/(2e^(501))) equals ...........

Let f(x) = x^(2) + 2x +5 and g(x) = x^(3) - 1 be two real functions. Find (f+g)(x), (f-g)(x), (fg)(x) and ((f)/(g))(x) .

Let f(x) = 3x^(2) + 6x + 5 and g(x) = x + 1 be two real functions. Find (f+g)(x), (f-g)(x), (fg)(x) and ((f)/(g))(x)

DISHA PUBLICATION-APPLICATION OF DERIVATIVES -EXERCISE - 2
  1. Find the intervals in which the function f given by f(x)=(4sinx-2x-xc...

    Text Solution

    |

  2. Let f(x)=x^3+ax^2+bx+5sin^2x be an increasing function in the set of r...

    Text Solution

    |

  3. The function f(x) = 3 cos^(4)x + 10 cos^(3) x + 6 cos^(2)x - 3, (0 le ...

    Text Solution

    |

  4. f(x) = 2x^(2) – log | x | (x != 0) is monotonic increasing in the int...

    Text Solution

    |

  5. The minimum value of e^((2x^(2)-2x+1)sin^(2)x) is

    Text Solution

    |

  6. The number of solutions of the equation x^3 +2 x^2 +5 x + 2 cos x = 0 ...

    Text Solution

    |

  7. Let g(x)=2f(x/2)+f(1-x) and f^(primeprime)(x)<0 in 0<=x<=1 then g(x)

    Text Solution

    |

  8. If f(x)=x+sinx ,g(x)=e^(-x),u=sqrt(c+1)-sqrt(c) v=sqrt(c) -sqrt(c-1),(...

    Text Solution

    |

  9. f(x)=(sin^(2)x)e^(-2sin^(2)x)*max f(x)-min f(x)=

    Text Solution

    |

  10. Given P(x)""=""x^4+""a x^3+""c x""+""d such that x""=""0 is the only ...

    Text Solution

    |

  11. L L ' is the latus sectum of the parabola y^2=4a xa n dP P ' is a doub...

    Text Solution

    |

  12. Let y=x^2 e^(-x) then the interval in which y increases with respect t...

    Text Solution

    |

  13. The function log(1+x) - (2x)/(x+2) is increasing in the interval:

    Text Solution

    |

  14. Prove that the function f(x)=tanx-4x is strictly decreasing on (-pi//3...

    Text Solution

    |

  15. Which one of the following statements is correct in respect of the cur...

    Text Solution

    |

  16. Tangent is drawn to ellipse (x^2)/(27)+y^2=1 at (3sqrt(3)costheta,sint...

    Text Solution

    |

  17. Let domain and range of f(x) and g(x) are respectively (0,oo). If f(x)...

    Text Solution

    |

  18. The volume V and depth x of water in a vessel are connected by the rel...

    Text Solution

    |

  19. Find the maximum value and the minimum value and the minimum value of ...

    Text Solution

    |

  20. Find the points of inflection for f(x)=sinx f(x)=3x^4-4x^3 f(x)=x...

    Text Solution

    |